Betting the Kelly Stake

Steadily growing your bank requires more than just knowing a good value bet when you see one, as you also need maximize your winnings as much as possible, without risking too much of your bankroll. If you’re simply a person than like to put down £10, £50, even £100 on a match now and again, you probably don’t need to concern yourself much with this (as long as you can afford to lose what you’re betting).

However, for serious punters, the question of how much to risk on any one bet becomes a heck of a lot more important. You obviously want to win as much as possible, but the bookmakers hate losing even more than you love winning. It’s a known fact that consistent winning is frowned upon, and in fact, to such an extent that most bookmakers will close accounts that win too often or else require them to pay high premiums.

This means that if you already know how to spot a good bet, you can’t
be wasting your time making a bunch of minor bets, as you should be
focused on maximizing your potential. Luckily many smart statisticians
have studied the problem before you and there are a number of methods
that can help to calculate exactly what you should stake on a given bet.

Knowing how to calculate your stakes for a given bet based on the
odds isn’t necessarily easy, and there are surely many different methods
used (although many people still surprisingly rely on a gut feeling
instead of simple statistics), but the most reliable means has to be
calculating the Kelly stake.

Kelly’s original work was purely theoretical statistics, calculated
based on repeated events with an exact probability. In order for it to
be applied, the bettor must have an advantage, which is why it obviously
couldn’t work at the roulette table, as the house always holds the
advantage.

Now you might be saying to yourself that bookmakers also hold an advantage, which is slightly true as they always offer inflated odds. However, being a smart punter is still about spotting when those odds differ enough from your estimated probability of that outcome to constitute a real value bet. Of course, this still doesn’t mean you should simply risk all of your bankroll, as there is always a fairly high chance you could lose—and this is where the Kelly stake can help.

Calculating the Kelly Stake

In the simplest of terms, Kelly’s strategy was that to maximize their
profits a bettor needs only to calculate their advantage and then bet
that percentage of their total bankroll. This would be simple in a
situation with fixed, exact odds, but it becomes slightly trickier in
sports betting, but nonetheless possible.

To see how it works, let’s say you are considering betting on Chelsea
to beat Liverpool in an upcoming match and a bookmaker is offering odds
of Chelsea: 11/10; Liverpool: 23/10; Draw: 5/2. Now,
to figure out how much you should bet, you need to calculate both the
bookmaker’s implied probability (in this case, 47.62%) and your own
estimate of Chelsea’s probability to win. If the odds are fractional as
these, you’ll also need to convert them to decimal odds (Chelsea: 2.10).

Now, you may think that Chelsea has a much better than 50% chance of
winning, but If you’re smart, your estimate and the bookmaker’s implied
probability shouldn’t be wildly off, even if you’re sure Chelsea will
win. For our purposes, let’s say you decide their probability of winning
is 52%.

Knowing these two probabilities and the total amount of your
bankroll, the appropriate Kelly stake can then be calculated using this
formula:

((Your Estimated Probability x Odds) – 1) / (Odds – 1)

So in our case: ((.52 x 2.10) – 1) / (2.10 – 1)

(1.092 – 1) / 1.10

.0092 / 1.10 =

0.08 or 8% Kelly stake

Using the Kelly Stake

Using this example, you should be wagering 8% of your total bankroll
for the full Kelly stake. Now this may not sound like much to some of
you, but in truth, even betting this much could actually see you lose a
significant portion of your bank if you hit a run of successive losses
(in fact, even with the Kelly stake, you have just as good of a chance
of losing half of your bankroll before you double it). Of course, this
also applies much more to those with a larger bankroll, as there is a
huge difference between £8, £80 and £800 bets.

The major issue is that many punters tend to overestimate their
advantage. We already mentioned how smart punters know that their
estimated advantage should always be close to the bookmaker’s, as even a
few percentage points can cost you some serious cash.

To help with this problem of overestimation, some punters use
half-Kelly or even quarter-Kelly bets, which in our case would be 4% or
2% of the total bankroll. These fractional Kelly stakes won’t grow your
bankroll as quickly, but they can also help prevent the huge downswings
that sometimes occur, or at least lessen their impact. While you have a 1
in 2 chance of losing half your bankroll before doubling it with the
full Kelly stake, these odds decrease all the way to 1 in 9 with
half-Kelly stakes, showing just how beneficial it can be.

There is no surefire strategy to make you an instant winner, as it’s really all about judging the value of a bet. Still, the Kelly strategy is surely one of the best ways for a good punter for maximize their earning potential.

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